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Guidance

We measure a line segment’s
length
with a ruler. Angles are measured with something called a
protractor
. A protractor is a measuring device that measures how “open” an angle is. Angles are measured in degrees, and labeled with a
symbol.

Notice that there are two sets of measurements, one opening clockwise and one opening counter-clockwise, from
to
. When measuring angles, always line up one side with
, and see where the other side hits the protractor. The vertex lines up in the middle of the bottom line, where all the degree lines meet.

For every angle there is a number between
and
that is the measure of the angle in degrees. The angle's measure is then the absolute value of the difference of the numbers shown on the protractor where the sides of the angle intersect the protractor. In other words, you do not have to start measuring an angle at
, as long as you subtract one measurement from the other.

The
Angle Addition Postulate
states that if
is on the interior of
, then
. See the picture below.

Drawing a
Angle with a Protractor

Start by drawing a horizontal line across the page, about 2 in long.

Place an endpoint at the left side of your line.

Place the protractor on this point. Make sure to put the center point on the bottom line of the protractor on the vertex. Mark
on the appropriate scale.

Copying an Angle with a Compass and Straightedge

We are going to copy the angle created in the previous investigation, a
angle. First, draw a straight line, about 2 inches long, and place an endpoint at one end.

With the point (non-pencil side) of the compass on the vertex, draw an arc that passes through both sides of the angle. Repeat this arc with the line we drew in #1.

Move the point of the compass to the horizontal side of the angle we are copying. Place the point where the arc intersects this side. Open (or close) the “mouth” of the compass so you can draw an arc that intersects the other side of the arc drawn in #2. Repeat this on the line we drew in #1.